Polytope of Type {39}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {39}*78
Also Known As : 39-gon, {39}. if this polytope has another name.
Group : SmallGroup(78,5)
Rank : 2
Schlafli Type : {39}
Number of vertices, edges, etc : 39, 39
Order of s₀s₁ : 39
Special Properties :
   Universal
   Spherical
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {39,2} of size 156
   {39,4} of size 312
   {39,6} of size 468
   {39,6} of size 624
   {39,4} of size 624
   {39,12} of size 1248
   {39,8} of size 1248
   {39,6} of size 1404
   {39,10} of size 1560
   {39,12} of size 1872
   {39,6} of size 1872
Vertex Figure Of :
   {2,39} of size 156
   {4,39} of size 312
   {6,39} of size 468
   {6,39} of size 624
   {4,39} of size 624
   {12,39} of size 1248
   {8,39} of size 1248
   {6,39} of size 1404
   {10,39} of size 1560
   {12,39} of size 1872
   {6,39} of size 1872
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {13}*26
   13-fold quotients : {3}*6
Covers (Minimal Covers in Boldface) :
   2-fold covers : {78}*156
   3-fold covers : {117}*234
   4-fold covers : {156}*312
   5-fold covers : {195}*390
   6-fold covers : {234}*468
   7-fold covers : {273}*546
   8-fold covers : {312}*624
   9-fold covers : {351}*702
   10-fold covers : {390}*780
   11-fold covers : {429}*858
   12-fold covers : {468}*936
   13-fold covers : {507}*1014
   14-fold covers : {546}*1092
   15-fold covers : {585}*1170
   16-fold covers : {624}*1248
   17-fold covers : {663}*1326
   18-fold covers : {702}*1404
   19-fold covers : {741}*1482
   20-fold covers : {780}*1560
   21-fold covers : {819}*1638
   22-fold covers : {858}*1716
   23-fold covers : {897}*1794
   24-fold covers : {936}*1872
   25-fold covers : {975}*1950
Permutation Representation (GAP) :

s0 := ( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)
(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39);;
s1 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)
(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38);;
poly := Group([s0,s1]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1");;
s0 := F.1;;  s1 := F.2;;  
rels := [ s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(39)!( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19)
(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39);
s1 := Sym(39)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)
(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38);
poly := sub<Sym(39)|s0,s1>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1> := Group< s0,s1 | s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope